| Abstract: |
| In this talk we consider the Cauchy problem of global in time existence of large strong solutions to the Navier Stokes equations for compressible viscous and heat conducting fluids. A class of density dependent viscosity is considered. By introducing the modified effective viscous flux and using the bootstrap argument, we establish the global existence of large strong solutions when the initial density is linearly equivalent to a large constant state. It should be mentioned that this result is obtained without any restrictions on the size of initial velocity and initial temperature. In addition, we establish the convergence of the solutions to its associated equilibrium with an explicit decay rate. |
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